Green-Schwarz mechanism and ${\alpha }^{\mathrm{\prime }}$-deformed Courant brackets

We establish that the unusual two-form gauge transformations needed in the Green-Schwarz anomaly cancellation mechanism fit naturally into an ${\alpha }^{\mathrm{\prime }}$-deformed generalized geometry. The algebra of gauge transformations is a consistent deformation of the Courant bracket and features a nontrivial modification of the diffeomorphism group. This extension of generalized geometry emerged from a `doubled ${\alpha }^{\mathrm{\prime }}$-geometry’, which provides a construction of exactly gauge and T-duality invariant ${\alpha }^{\mathrm{\prime }}$ corrections to the effective action.